def main():
""" Load and pre-process data. """
data_path = (
'C:\\Users\\Alexa\\Desktop\\KTH\\EGET\\Bayesian_Ben_Lambert\\GITHUB\\Solutions-to-Problems-in-Bayesian-Statistics\\All_data\\likelihood_blogVisits.csv'
)
time_between_visits = loadData(data_path)
""" Solution to question 4.1.4 """
MLE_first_time_visit_rate = compute_MLE_mean_time_between_visits(
time_between_visits)
print(
"The MLE of the first time visit rate for a blog, using 50 data points."
)
print("MLE estimate for lambda: ", MLE_first_time_visit_rate)
""" Solution to question 4.1.5 """
log_likelihoods, mean_visit_rates = log_likelihood_as_function_of_mean_visit_rate(
time_between_visits)
log_likelihood_MLE = compute_log_likelihoods(time_between_visits,
MLE_first_time_visit_rate)
plotter(
log_likelihoods, mean_visit_rates, MLE_first_time_visit_rate,
log_likelihood_MLE,
"The log likelihood as a function of the rate between first time visits",
"Avg no. visits per min", "log likelihood")
def main():
# data_path = ('C:\\Users\\Alexa\\Desktop\\KTH\\EGET\\Bayesian_Ben_Lambert\\GITHUB\\Solutions-to-Problems-in-Bayesian-Statistics\\All_data\\conjugate_epil.csv')
# epilepsy_data = loadData(data_path)
#
# epilepsy_counts = get_column(epilepsy_data["x"])
# a = 3
# b = 0.5
# data = [3, 7, 4, 10, 11]
#
# disease_outbreaks_model = Disease_outbreaks_model(a, b, data)
""" Q 10.1.1 The Gamma Prior """
# gamma_prior, lambda_range = disease_outbreaks_model.gamma_prior()
# plotter(lambda_range, gamma_prior, 'The prior '+ r'$\Gamma$' +'(3, 0.5)', r'$\lambda$', "pdf")
""" Q 10.1.2 The Gamma conjugate Prior of the Poisson Likelihood"""
# gamma_posterior, lambda_range = disease_outbreaks_model.gamma_prior()
# plotter(lambda_range, gamma_posterior, 'The posterior '+ r'$\Gamma$' +'(3 + 35, 0.5 + 5)', r'$\lambda$', "pdf")
""" Q 10.1.3-4 Posterior predictive"""
# no_iterations = 10000
# posterior_predictive_disease_outbreaks = disease_outbreaks_model.sample_posterior_predictive_distribution(no_iterations)
#
# # plotter_histogram(posterior_predictive_disease_outbreaks, 'No disease outbreaks', 'Frequency', 'Posterior Predictive distribution over disease outbreaks')
#
#
# print("Data maximum: ", np.max(data))
# print("Data minimum: ", np.min(data))
#
# print('Pr(T(fake) >= T(actual)_max | data) ', np.mean(np.array(posterior_predictive_disease_outbreaks) >= np.max(data)))
# print('Pr(T(fake) <= T(actual)_min | data) ', np.mean(np.array(posterior_predictive_disease_outbreaks) <= np.min(data)))
#
#
# """ Q 10.1.6 Posterior predictive"""
# print('Pr(T(fake) >= 20 | data) ', np.mean(np.array(posterior_predictive_disease_outbreaks) >= 20 ))
""" Q 10.1.7-8 Posterior predictive"""
a = 3
b = 0.5
data = [3, 7, 4, 10, 11, 20]
disease_outbreaks_model = Disease_outbreaks_model(a, b, data)
# New poserior
gamma_posterior, lambda_range = disease_outbreaks_model.gamma_prior()
plotter(lambda_range, gamma_posterior,
'The posterior ' + r'$\Gamma$' + '(3 + 35 + 20, 0.5 + 5 + 1)',
r'$\lambda$', "pdf")
no_iterations = 10000
posterior_predictive_disease_outbreaks = disease_outbreaks_model.sample_posterior_predictive_distribution(
no_iterations)
print('Pr(T(fake) >= 20 | data) ',
np.mean(np.array(posterior_predictive_disease_outbreaks) >= 20))
def main():
""" Load and pre-process data. """
data_path = (
'C:\\Users\\Alexa\\Desktop\\KTH\\EGET\\Bayesian_Ben_Lambert\\GITHUB\\Solutions-to-Problems-in-Bayesian-Statistics\\All_data\\likelihood_NewYorkCrimeUnemployment.csv'
)
crime_dataframe = loadData(data_path)
population = convert_str_to_int(reshape_data(
crime_dataframe["Population"]))
violent_crime_count = convert_str_to_int(
reshape_data(crime_dataframe["Violent_crime_count"]))
plotter(population, violent_crime_count, "population",
"violent crime count")
""" Problem 4.2.3 """
MLE_estimate = MLE_estimator(violent_crime_count, population)
print("The MLE is:", MLE_estimate)
def main():
""" Load and pre-process data. """
data_path = (
'C:\\Users\\Alexa\\Desktop\\KTH\\EGET\\Bayesian_Ben_Lambert\\GITHUB\\Solutions-to-Problems-in-Bayesian-Statistics\\All_data\\likelihood_blogVisits.csv'
)
time_between_visits = loadData(data_path)
""" Solution to question 4.1.4 """
MLE_first_time_visit_rate = compute_MLE_mean_time_between_visits(
time_between_visits)
print(
"The MLE of the first time visit rate for a blog, using 50 data points."
)
print("MLE estimate for lambda: ", MLE_first_time_visit_rate)
"""Generating data using the MLE parameter for the visit rate to evaluate our model"""
generated_beer_visits = generate_data_samples(
1 / MLE_first_time_visit_rate, len(time_between_visits))
# Plotting the generated data against the actual data
plotter(generated_beer_visits, time_between_visits)
def main():
""" Load and pre-process data. """
data_path = (
'C:\\Users\\Alexa\\Desktop\\KTH\\EGET\\Bayesian_Ben_Lambert\\GITHUB\\Solutions-to-Problems-in-Bayesian-Statistics\\All_data\\denominator_NBCoins.csv'
)
crime_dataframe = loadData(data_path)
failuers_before_five_successes = convert_str_to_int(
reshape_data(crime_dataframe["No failuers before 5 successes"]))
theta1_range = np.arange(0.001, 0.999, 0.01)
theta2_range = np.arange(0.001, 0.999, 0.01)
""" Compute the likelihood over the theta_1 and theta_2 ranges. """
likelihoods = compute_likelihood(failuers_before_five_successes,
theta1_range, theta2_range)
""" Create a contour plot over the rwo theta values."""
plotter(
theta1_range, theta2_range, likelihoods,
r'The posterior shape over $\theta_1$ and $\theta_2$ for the Negative Binomial likelihood',
r"$\theta_1$", r"$\theta_2$")
def main():
""" Load and pre-process data. """
data_path = ('C:\\Users\\Alexa\\Desktop\\KTH\\EGET\\Bayesian_Ben_Lambert\\GITHUB\\Solutions-to-Problems-in-Bayesian-Statistics\\All_data\\posterior_gdpInfantMortality.csv')
GDP_data = loadData(data_path)
mortality_data = get_column(GDP_data["infant.mortality"])
gdp_data = get_column(GDP_data["gdp"])
# Remove data points with missing data i.e. NaN values.
gdps, mortalities = remove_missing_data(gdp_data, mortality_data)
# Fit the data to a normal distribution model i.e. least squares.
gdp_log_range, mortality_log_values, intercept, slope = fit_normal_dist_model(
gdps, mortalities)
# Plot the log(data) and the model.
plotter(np.log(mortalities), np.log(gdps), "log(mortalities)", 'log(GDP)', gdp_log_range, np.array(mortality_log_values).reshape(-1),
"A Normal Distribution fit to the logged data - alpha " + str(round(intercept, 3)) + " beta " + str(round(slope, 3)))
calculate_standard_error(np.log(gdps), np.log(mortalities))
calculate_RMSE(gdps, mortalities, intercept, slope)
def main():
data_path = (
'C:\\Users\\Alexa\\Desktop\\KTH\\EGET\\Bayesian_Ben_Lambert\\GITHUB\\Solutions-to-Problems-in-Bayesian-Statistics\\All_data\\conjugate_epil.csv'
)
epilepsy_data = loadData(data_path)
epilepsy_counts = get_column(epilepsy_data["x"])
a = 4
b = 0.25
eilepsy_model = Epilepsy_model(a, b)
""" Q 9.2.3 The Gamma Posterior """
# posterior, theta_range = eilepsy_model.posterior_gamma(epilepsy_counts)
#
# plotter(theta_range, posterior, "Gamma(a + " +r'$\sum^n_{i=1}(x_i)$'+", b + n) posterior over " + r'$\theta$', r'$\theta$', "pdf")
""" Q 9.2.5 The Gamma Posterior Predictive distribution """
posterior_NB, theta_range = eilepsy_model.posterior_predictive_gamma(
epilepsy_counts)
plotter(
theta_range, posterior_NB, "Gamma(a + " + r'$\sum^n_{i=1}(x_i)$' +
", b + n) posterior over " + r'$\theta$', r'$\theta$', "pdf")
def main():
""" The Multinomial Likelihood for n_A = 6, n_B = 3 and n_C = 1 """
Election_Likelihood_Model = Election_model(6, 3, 1, 10)
likelihoods, pB_range, pA_range = Election_Likelihood_Model.compute_multinomial_likelihood()
plotter(pA_range, pB_range, likelihoods,
"Multinomial Likelihood over " + r'$p_A$' + " and " + r'$p_B$' , r'$p_A$' , r'$p_B$')
""" The Conjugate Dirichlet(1, 1, 1) prior """
priors, pB_range, pA_range = Election_Likelihood_Model.dirichlet_prior(1, 1, 1)
plotter(pA_range, pB_range, priors,
"Dirichlet prior using " + r'$\alpha_A, \alpha_B, \alpha_C = 1 $' + " for "+ r'$p_A$' +" and " + r'$p_B$' , r'$p_A$' , r'$p_B$', plt.cm.YlGnBu)
""" The Dirichlet(1, 1, 1) posterior """
posterior, pB_range, pA_range = Election_Likelihood_Model.dirichlet_posterior(
1, 1, 1)
plotter(pA_range, pB_range, posterior,
"Posterior with Multinomial Likelihood and Dirichlet(1, 1, 1) prior over " + r'$p_A$' + " and " + r'$p_B$', r'$p_A$', r'$p_B$')
""" Posterior Mean using Dirichlet uniform prior"""
posterior_mean_dirichlet_uniform_prior = Election_Likelihood_Model.posterior_mean(
1, 1, 1)
print("Posterior mean parameters: p_A = ", posterior_mean_dirichlet_uniform_prior[0], " p_B = ", posterior_mean_dirichlet_uniform_prior[1], " p_C = ", posterior_mean_dirichlet_uniform_prior[2])
""" The Conjugate Dirichlet(10, 10, 10) prior """
priors, pB_range, pA_range = Election_Likelihood_Model.dirichlet_prior(10, 10, 10)
plotter(pA_range, pB_range, priors,
"Dirichlet(10, 10, 10) prior using " + r'$\alpha_A, \alpha_B, \alpha_C = 1 $' + " for "+ r'$p_A$' +" and " + r'$p_B$' , r'$p_A$' , r'$p_B$', plt.cm.YlGnBu)
""" The Dirichlet(10+6, 10+3, 10+1) posterior """
posterior, pB_range, pA_range = Election_Likelihood_Model.dirichlet_posterior(
10, 10, 10)
plotter(pA_range, pB_range, posterior,
"Posterior with Multinomial Likelihood and Dirichlet(10, 10, 10) prior over " + r'$p_A$' + " and " + r'$p_B$', r'$p_A$', r'$p_B$')
""" The Multinomial Likelihood for n_A = 60, n_B = 30 and n_C = 10 """
Election_Likelihood_Model = Election_model(60, 30, 10, 100)
likelihoods, pB_range, pA_range = Election_Likelihood_Model.compute_multinomial_likelihood()
plotter(pA_range, pB_range, likelihoods,
"Multinomial Likelihood over " + r'$p_A$' + " and " + r'$p_B$' , r'$p_A$' , r'$p_B$')
""" The Dirichlet(10 + 60, 10 + 30, 10 + 10) posterior """
posterior, pB_range, pA_range = Election_Likelihood_Model.dirichlet_posterior(
10, 10, 10)
plotter(pA_range, pB_range, posterior,
"Posterior Dirichlet(10 + 60, 10 + 30, 10 + 10) with Multinomial Likelihood and Dirichlet(10, 10, 10) prior over " + r'$p_A$' + " and " + r'$p_B$', r'$p_A$', r'$p_B$')